On the direct insulatorquantum Hall transition in twodimensional electron systems in the vicinity of nanoscaled scatterers
 ChiTe Liang^{1}Email author,
 LiHung Lin^{2},
 Chen Kuang Yoa^{1},
 ShunTsung Lo^{1},
 YiTing Wang^{1},
 DongSheng Lou^{3},
 GilHo Kim^{4},
 Chang YuanHuei^{1},
 Yuichi Ochiai^{5},
 Nobuyuki Aoki^{5},
 JengChung Chen^{3},
 Yiping Lin^{3},
 Huang ChunFeng^{6},
 ShengDi Lin^{7} and
 David A Ritchie^{8}
DOI: 10.1186/1556276X6131
© Liang et al; licensee Springer. 2011
Received: 14 August 2010
Accepted: 11 February 2011
Published: 11 February 2011
Abstract
A direct insulatorquantum Hall (IQH) transition corresponds to a crossover/transition from the insulating regime to a high Landau level filling factor ν > 2 QH state. Such a transition has been attracting a great deal of both experimental and theoretical interests. In this study, we present three different twodimensional electron systems (2DESs) which are in the vicinity of nanoscaled scatterers. All these three devices exhibit a direct IQH transition, and the transport properties under different nanaoscaled scatterers are discussed.
Introduction
The simultaneous presence of disorder and a strong enough magnetic field B can lead to a wide variety of interesting physical phenomena. For example, the integer quantum Hall effect is one of the most exciting effects in twodimensional electron systems (2DES), in which the electrons are usually confined in layers of the nanoscale [1]. In an integer quantum Hall (QH) state, the current is carried by the onedimensional edge channels because of the localization effects. It has been shown that with sufficient amount of disorder, a 2DES can undergo a Binduced insulator to quantum Hall transition [2–5]. Experimental evidence for such an insulatorquantum Hall (IQH) transition is an approximately temperature (T)independent point in the measured longitudinal resistivity of a 2DES [3–5]. The IQH transition continues to attract a great deal of interest both experimentally and theoretically as it may shed light on the fate of extended states [6–10], the true ground state of a noninteracting 2DES [2], and a possible metalinsulator transition in 2D [11, 12].
It is worth pointing out that in order to observe an IQH transition separating the zerofield insulator from the QH liquid, one needs to deliberately introduce strong disorder within a 2DES. The reason for this is that the localization length needs to be shorter than the sample size. In the study by Jiang and coworkers [2], a 2DES without a spacer layer in which strong Coulomb scattering exists was used. Wang et al. utilized a 30nmthick heavily doped GaAs layer so as to allow the positively charged Si atoms to introduce longrange random potential in the 2DES [3]. Hughes et al. have shown that when a Sidoped plane was incorporated into a 550nmthick GaAs film, a deep potential well can form in which the 2DES is confined close to the ionized donors and is therefore highly disordered [4]. It has been shown that by deliberately introducing nanoscaled InAs quantum dots [13] in the vicinity of a modulationdoped GaAs/AlGaAs heterostructure, a strongly disordered 2DES which shows an IQH transition can be experimentally realized [14, 15].
The transition/crossover from an insulator to a QH state of the filling factor ν > 2 in an ideal spinless 2DES can be denoted as the direct IQH transition [16–19]. Such a transition has been attracting a great deal of interest and remains an unsettled issue. Experimental [16–19] and theoretical results [9, 10] suggest that such a direct transition can occur, and it is a quantum phase transition. However, Huckestein [20] has argued that such a direct transition is not a quantum phase transition, but a narrow crossover in B due to weak localization to Landau quantization.
In this study, the authors compare three different electron systems containing nanoscaled scatterers which all show a direct IQH transition. The first sample is a GaAs 2DES containing selfassembled nanoscaled InAs quantum dots [13, 14, 21–23].
The second one is a 2DES in a nominally undoped AlGaN/GaN heterostructure [24–33] grown on Si substrate [33, 34]. Such a GaNbased electron system can be affected by nanoscaled dislocation and impurities [35]. Finally, experimental results on the third sample, a deltadoped GaAs/AlGaAs quantum well with additional modulation doping [36, 37], will be presented. All the experimental results on the three completely different samples show that the direct IQH transition does not occur with the onset of strong localization due to Landau quantization [20, 38]. Therefore, in order to obtain a thorough understanding of the direct IQH transition, further studies are required.
Experimental details
Results and discussions
It has been suggested that by converting the measured resistivities into longitudinal and Hall conductivities, it is possible to shed more light on the observed IQH transition [5]. Figure 6 shows such results at various temperatures. Interestingly, for B < 5 T, _{σ} _{ xy } is nominally T independent. Such data are consistent with electronelectron interaction effects. Over the whole measurement range, σ_{ xx } decreases with increasing T, consistent with electronelectron interaction effects. Unlike σ_{ xy }, σ_{ xx } shows a significant T dependence.
Conclusions
In conclusion, the authors have presented studies on three completely different electron systems. In these three samples, the nanoscaled scatterers, in close proximity of the 2DES, provide necessary disorder for observing the direct IQH transition. In these studies, it has been shown that the crossover from localization to Landau quantization actually covers a wide range of magnetic field. Moreover, the observed direct IQH transition is not necessarily linked with Landau quantization as no resistance oscillations are observed even up to a magnetic field 4 T higher than the crossing field. Most importantly, the onset of strong localization which gives rise to the formation of quantum Hall state does not correspond to the direct IQH transition. All these three pieces of experimental evidence show that a 2DES in the vicinity of nanoscaled scatterers is an ideal playground for studying the direct IQH transition. Furthermore, in order to obtain a thorough understanding of the underlying physics of the direct IQH transition, modifications of Huckestein's model [20] must be made.
Abbreviations
 IQH:

insulatorquantum Hall
 SdH:

Shubnikovde Haas
 2DESs:

twodimensional electron systems.
Declarations
Acknowledgements
This research was supported by the WCU (World Class University) program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. R322008000102040). C.T.L. acknowledges financial support from the NSC (Grant no: NSC 992119M002018MY3). The authors would like to thank YiChun Su and JauYang Wu for providing help in the experiments.
Authors’ Affiliations
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